Wireless communication systems typically include transmitters that have to generate signals which are strictly limited to the specified frequency channel in order to avoid interference with other users. For this reason, the transmitters typically have radio frequency filters in order to attenuate interference signals between different communication systems such as GSM (global system for mobile communication) and the transmitting and receiving channels within a system. The interference between different users operating within the same channel is limited by the use of base band filters. Since the maximum data transfer speed is correlated to the performance of the base band filters, they can become a bottleneck of the performance of the whole system and further result in high circuit complexity.
Current state-of-the-art implementation would be to use in the transmitter a base band filter having a small amplitude variation, e.g. 0.1 dB ripple, in the pass band or the frequency band which is occupied by the wanted signal. The stop band attenuation is usually specified by regulations which define the spectral purity so as to typically limit the maximum out-of-band spectral power which otherwise can harm other radio frequency usage. A main problem is that small amplitude ripple in pass band and typically high requirement for stop band attenuation result in the provision of a filter apparatus having a long impulse response in time domain, which means that the signal energy will be distributed in time domain so that part of the energy which is in one transmitted symbol may leak to the next symbol causing inter-symbol-interference.
Both digital and analog base band filters have a trade-off between a wanted behavior e.g. with regard to base-band spectral flatness and stop-band attenuation, an unwanted behavior e.g. with regard to a distortion of the signal and the length of the impulse response of the filter apparatus and the complexity of the filter apparatus. High order filters result in low amplitude variation in the pass-band and high stop-band rejection, but also have a long impulse response which spreads the filtered signal energy in time domain, and further require complex circuitry. A system with low order filtering, however, results in poor spectral efficiency, since the separation between different users in frequency domain must be increased to avoid interference. On the other hand, long impulse responses created by high order filtering cause signal spreading in time domain, which results in inter-symbol interference or requires longer guard intervals between transmitted symbols, both of which limit the speed of the data transfer.